_{to prove (r=1 to r=7)}∑tan² rπ/16=35

Start by combining pi/8 and 7pi/8, 3pi/16 and 5pi/16; 3pi/16 and 5pi/16 terms to get Tan2A form. You can do so either in tan-cot or Sin Cos conversion also.

Once, through with this step, do this again by combining complimentary terms to get 2A form of the trig. ratios. which will eventually lead to a number.